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4014 12

PM guideway I

90

36

9

16

PM guideway C

61

33

10

16

PM guideway B

57

2714 18

PM guideway A

Optimization of the Superconducting Linear

Magnetic Bearing of a Maglev Vehicle

Loïc Quéval

1

, Guilherme G. Sotelo

2

, Y. Kharmiz

1

, Daniel H.N. Dias

2

, Felipe Sass

2

,

Purpose

1 Lab for Electrical Machines, University of Applied Sciences, Düsseldorf, Germany.

2 Fluminense Federal University, Niterói (RJ), Brazil.

3 Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany.

Develop and validate a 3D FE model of a superconducting linear magnetic bearing.

Reduce the 3D model to a 2D model to decrease the computing time while keeping a good accuracy.

Use the 2D model to optimize the bearing cost considering a displacement sequence.

Modeling

PM guideway model

Conclusion

We developed a superconducting linear magnetic bearing 3D finite element model. It is

based on the H-formulation with a power law E-J relationship. The J

c

(B) dependence, the PM

guideway real geometry and the iron nonlinearity are included. The model is validated by

comparison with experimental data. For the optimization, the 3D model is reduced to a 2D

model by shortening artificially its length, instead of decreasing the critical current density.

Taking the SupraTrans prototype bearing as reference, the PM guideway optimization results

show that it is possible to greatly reduce the cost for the same performances on a given

displacement sequence; or to greatly improve the performances for the same cost.

Víctor M.R. Zermeno

3

, Raimund Gottkehaskamp

1

ID: 3A-LS-P-04.03

From 3D to 2D

It is common practice to calibrate the critical current density J

c0

of the bulk using the

maximum levitation force measured during the ZFC sequence.

Parametrization

We consider the bearing initially designed and optimized for the SupraTrans maglev vehicle

demonstrator.

HTS bulk model

SLMB model

(a) Zero field cooling

(b) Vertical displacement downward

(c) Vertical displacement upward.

(a) Field cooling

(b) Vertical displacement downward

(c) Lateral displacements.

Validation

What: Permanent magnets and iron pieces

arranged in flux concentrator.

How: 2D magnetostatic FEM

- iron nonlinear BH curve

- real geometry.

What: 3-seeded melt-textured YBCO block.

How: 2D or 3D H-formulation FEM

- power law E-J relationship

- isotropic Kim like model Jc(B)

- 3 independent domains.

How: Unidirectional coupling between HTS bulk

model and PM guideway model.

- only 1 static solution of the PM guideway model

- reduced LN

2

domain around HTS bulk.

Objective and constraints

Optimization

3D model 2D model

with reduced J

c0

with reduced d

Results

2D model

Dimensions of PM guideway : 4 parameters

Dimensions of HTS bulk : unchanged

Computing time < 1 min

We look for the PM guideways that minimize the cost of the guideway and maximize the

lateral force during LD sequence, with a constraint on the minimum levitation force,

Multi-objective Particule Swarm Optimization (PSO)

- 100 particules

- 25 generations

Total computing time ~40 h

Optimization algorithm

Fig. 1 - SLMB Geometry.

Fig. 2 - Magnetic flux density above the PM guideway

at z = 1, 5, 10, 20 mm.

Fig. 3 - Levitation force for ZFC sequence.

Fig. 4 - Lateral force for LD sequence.

Fig. 5 - Levitation force for LD sequence.

Note: The decrease of the levitation force during lateral displacements should be taken into

account during the optimization.

"Optimization on a displacement sequence"

5 mm

ZFC sequence

LD sequence

5 mm

25 mm 100 mm

10 mm

Fig. 8 - Initial and optimized PM guideways.

Dimensions in mm (on scale).

with

where , , .

cost [€/m]

F

y,max

[N]

PM guideway I

PM guideway A

PM guideway B

PM guideway C

1005

1012

1628

83

83

129

776

-23 %

99

+38 %

Fig. 7 - Bi-objective optimization results.

~

Fig. 6 - Parametrization of the PM guideway.

b

ac d